Does the president salute?

Yes you do. In the US Military, personal salute Comissoned Warrant officers, and Comissed officers, Foreign friendly Military members, The President, and medal of honor recipients. Like if you earned...

The President may (at his discretion) salute anyone he likes, although this is normally reserved for recipients of the Medal of Honor.

In the US, the President is defined as a member of the military; specifically, the highest possible rank. Saluting is expected.

As Commander in Chief of the military, the President returns salutes of Unit Commanders when bearing the flag or otherwise and honors the flag with a hand over heart when it is passing via a group...

The president only salutes Medal of Honor recipients